Urn I contains eleven black and nine white balls and urn II contains three black, eight white, and six red balls. Roll a fair die.

If the die is a one, three, or five, randomly select a ball from urn I. However, if the die is a two, four, or six, randomly select a ball from urn II.

(a) Determine the probability that the ball is black by drawing a tree diagram.

(b) Determine the probability that the ball is black using the Rule of Total Probability.

(c) If a randomly chosen ball is black, what is the probability that the ball came from urn I?

(d) If a randomly chosen ball is red, what is the probability that the ball came from urn I? urn II?